Let's assume it is a fools game. What kind of performance should we expect?

If your fund manager took 5 assets and randomly weighted them (i.e. she is a monkey) each period and repeated this over and over again we should end up with performance converging to an equally weighted portfolio. I.e. each asset would on average make up 20% of your holdings.

The equally weighted portfolio is the benchmark for any timing strategy (beat the monkey!).

If you are timing only one asset, the second 'asset' is cash as we invest more or less than all our portfolio in the asset. The baseline is 50% cash and 50% asset on average.

What if the underlying assets moved completely randomly instead? - i.e. forecasts of future returns, volatilities or correlations are more harmful than helpful.

It turns out that the equally weighted portfolio is the best response to such a landscape - implicitly we are assuming positive returns and beneficial diversification over time, but not much else.

From both extremes (and probably some areas in between) we end up with equally weighted portfolios.